Profit and Loss – Split sale (part at loss, part at gain) to break even: A shopkeeper buys books worth ₹ 750 in total. He sells two-fifths of them at a 15% loss. At what gain percentage should he sell the remaining books so that overall there is neither profit nor loss?

Introduction / Context:
We allocate a total purchase cost across two groups. The first group is sold at a known loss, so we can compute its realized revenue. To break even overall, the second group must contribute enough extra to offset that loss. This converts to a direct percentage gain requirement on the remaining portion.

Given Data / Assumptions:

• Total cost = ₹ 750
• Two-fifths sold at a 15% loss
• Objective: overall no profit and no loss

Concept / Approach:
Compute cost and revenue for the first portion, then find the revenue required from the remaining portion to reach exactly ₹ 750 in total revenue. Convert that required revenue into a percentage gain over its cost.

Step-by-Step Solution:
Cost of first part = (2/5) * 750 = ₹ 300Revenue from first part = 0.85 * 300 = ₹ 255Remaining cost = 750 − 300 = ₹ 450Required revenue from remainder = 750 − 255 = ₹ 495Gain% on remainder = (495 − 450) / 450 * 100 = 10%

Verification / Alternative check:
Total revenue 255 + 495 = 750 equals total cost 750, confirming break-even.

Why Other Options Are Wrong:
9% and 8% are not enough to offset the early loss; 12% and 15% would create an overall profit.

Common Pitfalls:
Applying 15% to the whole rather than just the fraction sold at a loss.

Final Answer:
10%